臺灣博碩士論文加值系統

After the discovery of graphene, condensed matter research community interact a lot to investigate two dimensional (2D) physics because of the unique chiral nature of its carrier dynamics and huge Landau level spacing in comparison to GaAs. For metrology application point of view, graphene on silicon carbide (SiC) has been identified as an ideal platform for resistance standards using particularly quantum Hall effect technique. This thesis describes the fabrication technique of epitaxial graphene-based millimeter-scale, series and parallel p-n junction device. And perform the quantum Hall effect measurement. These experiments elucidate some interesting physical properties and technological applications of graphene.

Epitaxial graphene (EG) on SiC, grown on hexagonal SiC at 1850 ºC temperatures, is nearly defect-free and mono-layer on the centimeter scale. It exhibits properties that are suitable for large-scale and high-current applications. We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene p-n-p junction devices using simple ultraviolet photolithography, thereby significantly reducing the device processing time compared to electron beam lithography typically used for obtaining approximately 200 nm wide dissipation less junctions. This work presents the resulting variety of experimental data obtained from these devices, introducing multiple current inputs with several different configurations. Furthermore, we use the LTspice circuit simulator to examine the various rearrangements of the electric potential in the device when injecting current at up to three independent sites. These measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at ν=2 plateau (R_H=h⁄(〖(2e〗^2)) , where R_H is the Hall resistance, h is the Planck constant and e is the electron charge) that take the form: a/b R_H. Here, a and b have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of R_H. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.

To verify the proposed UV photolithography technique, dissipation less junction and to support our non-conventional quantized Hall resistance values, we fabricated two more devices with four and seven p-n junction in series at millimeter scale. The utilization of single current in device through source and drain has enabled many integer (1, 2, 3, 4, 5, 6, 7 and 8) multiple of the quantized Hall resistance at ν=2 plateau (R_H≈ 12906 Ω).The usage of multiple current terminals and their arbitrarily selected placement on millimeter-scale graphene p-n junction devices has enabled the measurement of many fractional (2/3, 8/7, 6/17, 12/13, 24/29, 32/57 and many more) multiples of the R_H at ν=2 plateau. These integers and fractions can be determined both analytically and by simulations. These experiments validate the use of either the LTspice circuit simulator or the analytical framework recently presented in similar work. Furthermore, the production of several devices with large-scale junctions substantiates the approach of using simple ultraviolet lithography to obtain junctions of sufficient sharpness.

Measurements of fractional multiples of the ν=2 plateau quantized Hall resistance (R_H ≈ 12906 Ω) were enabled by the utilization of multiple current terminals on millimeter-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically generated with the LTspice circuit simulator. From the devices’ functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimeter or centimeter scale is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography.

After the discovery of graphene, condensed matter research community interact a lot to investigate two dimensional (2D) physics because of the unique chiral nature of its carrier dynamics and huge Landau level spacing in comparison to GaAs. For metrology application point of view, graphene on silicon carbide (SiC) has been identified as an ideal platform for resistance standards using particularly quantum Hall effect technique. This thesis describes the fabrication technique of epitaxial graphene-based millimeter-scale, series and parallel p-n junction device. And perform the quantum Hall effect measurement. These experiments elucidate some interesting physical properties and technological applications of graphene.

Epitaxial graphene (EG) on SiC, grown on hexagonal SiC at 1850 ºC temperatures, is nearly defect-free and mono-layer on the centimeter scale. It exhibits properties that are suitable for large-scale and high-current applications. We have demonstrated the millimeter-scale fabrication of monolayer epitaxial graphene p-n-p junction devices using simple ultraviolet photolithography, thereby significantly reducing the device processing time compared to electron beam lithography typically used for obtaining approximately 200 nm wide dissipation less junctions. This work presents the resulting variety of experimental data obtained from these devices, introducing multiple current inputs with several different configurations. Furthermore, we use the LTspice circuit simulator to examine the various rearrangements of the electric potential in the device when injecting current at up to three independent sites. These measurements yield nonconventional, fractional multiples of the typical quantized Hall resistance at ν=2 plateau (R_H=h⁄(〖(2e〗^2)) , where R_H is the Hall resistance, h is the Planck constant and e is the electron charge) that take the form: a/b R_H. Here, a and b have been observed to take on values such 1, 2, 3, and 5 to form various coefficients of R_H. These results support the potential for drastically simplifying device processing time and may be used for many other two-dimensional materials.

To verify the proposed UV photolithography technique, dissipation less junction and to support our non-conventional quantized Hall resistance values, we fabricated two more devices with four and seven p-n junction in series at millimeter scale. The utilization of single current in device through source and drain has enabled many integer (1, 2, 3, 4, 5, 6, 7 and 8) multiple of the quantized Hall resistance at ν=2 plateau (R_H≈ 12906 Ω).The usage of multiple current terminals and their arbitrarily selected placement on millimeter-scale graphene p-n junction devices has enabled the measurement of many fractional (2/3, 8/7, 6/17, 12/13, 24/29, 32/57 and many more) multiples of the R_H at ν=2 plateau. These integers and fractions can be determined both analytically and by simulations. These experiments validate the use of either the LTspice circuit simulator or the analytical framework recently presented in similar work. Furthermore, the production of several devices with large-scale junctions substantiates the approach of using simple ultraviolet lithography to obtain junctions of sufficient sharpness.

Measurements of fractional multiples of the ν=2 plateau quantized Hall resistance (R_H ≈ 12906 Ω) were enabled by the utilization of multiple current terminals on millimeter-scale graphene p-n junction devices fabricated with interfaces along both lateral directions. These quantum Hall resistance checkerboard devices have been demonstrated to match quantized resistance outputs numerically generated with the LTspice circuit simulator. From the devices’ functionality, more complex embodiments of the quantum Hall resistance checkerboard were simulated to highlight the parameter space within which these devices could operate. Moreover, these measurements suggest that the scalability of p-n junction fabrication on millimeter or centimeter scale is feasible with regards to graphene device manufacturing by using the far more efficient process of standard ultraviolet lithography.

Abstract iii
Acknowledgments v
List of Publications vii
Table of Contents ix
List of figures xiii
Chapter 1. Introduction 1
1.1 Background 1
1.2 Objective 2
1.3 Complexity 3
1.4 Methodology 3
Chapter 2. Background on the classical and quantum Hall effect 5
2.1 Classical Hall effect 5
2.2 The quantum Hall effect in two-dimensional electron systems 8
2.2.1 Landau quantization 10
2.2.2 Edge states 14
2.3 The quantum Hall effect in monolayer graphene 16
2.3.1 Band structure of graphene 17
2.3.2 Landau quantization in graphene 25
2.4 The quantum Hall effect in graphene p-n Junction 28
2.4.1 Evolution of the Landau levels across the p-n junctions 28
2.4.2 Theoretical calculation of a p-n-p junction 30
2.5 LTspice simulations 35
Chapter 3. Experimental techniques and optical characterization 39
3.1 Materials and experimental tools 39
3.2 Labelling on the carbon face of SiC before dicing the SiC wafer 40
3.3 Dicing and cleaning SiC wafer prior to growing graphene 40
3.4 Epitaxial monolayer graphene grown on centimeter scale 41
3.4.1 Confocal microscopy characterization 42
3.4.2 Atomic force microscopy 44
3.4.3 Raman spectroscopy 44
3.5 Fabrication of devices for quantum Hall measurement 45
3.6 Functionalisation of graphene by Cr(CO)3 48
3.7 Fabrication of p-n junctions on millimeter scale 49
3.7.1 Designing and making p-n junction optical masks 50
3.7.2 Series p-n junction 51
3.7.3 Checkerboard p-n junctions 52
3.8 Ultraviolet light exposer on p-n Junctions 53
3.9 Low-temperature transport measurement setup 54
3.9.1 Janis Cryogenic system 55
3.9.2 Four-terminal resistance measurement techniques 57
Chapter 4. Atypical quantized resistance in millimeter-scale epitaxial graphene p-n junctions 59
4.1 Verifying the charge configuration 59
4.2 Assessing the quality of the charge configuration and p-n junctions 60
4.3 Basic electrical characterization of p-n junctions 64
4.4 Measuring nonconventional fractions of the v=2 quantized Hall resistance 68
Chapter 5. Accessing ratios of the ν = 2 quantized Hall resistance in graphene p-n junction devices with multiple current terminals 73
5.1 Results on a four junction device 73
5.1.1 Optical Characterization 74
5.1.2 Electrical Verification 75
5.1.3 Using multiple terminals 77
5.2 Results on a seven junction device 79
5.2.1 Verifying the electrical functionality of all seven regions 79
5.2.2 Integer and fractional values of RH for a seven junction device 80
Chapter 6. Quantum Hall effect in graphene-based checkerboard p-n junction devices 83
6.1 Resistance of graphene-based checkerboard p-n junction devices 83
6.2 Hall resistance quantization using multiple current sources 86
6.3 Prediction of LT spice simulations 88
6.3.1 Proposing different region geometries 89
Chapter 7. Summary and outlook 91
References 95
Appendix 112
A 112
B 120
C 126
D 130

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